this is just going to keep happening.
buy a cheap car and it will either a) die completely or b) breakdown sufficiently enough that it costs more to fix it than to repair...
either way you'll need to get a another car.
so, do you keep throwing money away on bomb-cars that aren't worth maintaining or do you fork out more and buy a newer car that is more likely to keep running on you? A guy in my Rover crew (senior scouts) would buy $600 bombs and go through 3 or 4 cars *every year*!! He did that for years and years and we all thought he was mad...
I had this exact problem when I bought my first coupla cars. ('76 Ford Cortina, then a '74 Holden Torana) They were both cheap and nasty under $3k and I had each one for about a year at best before it was time to get rid of it. Eventually I borrowed money off mum and dad ($6k - had to pay them back slowly over the next 4 years) and bought a better car overall ('79 Nissan Stanza) and ended up driving that one for the next 9 years. My next car after that one was my first Camry for $12k (dummy'll remember that one) and I drove that for 10 years.
basically you get what you pay for but you need to think of the long term economics of the decision.
and as for a recommendation - a toyota camry or corrolla is usually a good car and reasonably reliabel